What to submit and when:

- All submissions are electronic: by e-mail to elenam at morris.umn.edu and CC to all lab partners. Please do not delete your e-mail from "Sent mail" or your mailbox until the end of the semester.
- When working on the lab, please comment your work so that it is clear what contributions of each person are.
- At the end of the lab each group should send me the results of their in-class work. Please indicate if this is your final submission.
- If your submission at the end of the lab time was not final, please send me(CC to the lab partner(s)) a final copy before the due time. Please use the subject "3501 Lab N", where N is the lab number.

Work in pairs

The goal of the lab is to practice with JFLAP (a tool for experimenting with finite automata and other computability topics) and to explore the pumping lemma for regular languages.

- Please save your automata files as .jff files and your data as
.txt files.
**Files names must be as follows**: names of those in the group followed by question name, e.g.`SmithAdams3.jff`

(where 3 refers to the question number). This will help me in running test data - Consult the JFLAP tutorial as needed.

The pumping lemma in JFLAP is implemented as a two-player "game" when one player is trying to prove that a language is regular by representing strings as required by the pumping lemma, and the other player is trying to disprove it, as described in the tutorial Regular Pumping Lemmas.

Go to "Regular Pumping Lemma" in the JFLAP start menu (careful: you
don't want Context-Free Pumping Lemma). There is a list of languages,
some are regular, some aren't. The alphabet is a,b. The pumping length is
denoted as m. JFLAP allows you to save the file with the log of all
your attempts. Please submit these files for the two cases below and
**additionally** write down your conclusions in a
plain-text file or an e-mail message.

Your conclusions should include:

- whether the language satisfies the pumping lemma. This is a bit tricky since you are testing a pumping length, but your conclusions should be general. For a language that satisfies the pumping lemma show its pumping length and explain how you would always be able to break down a string that in a way that satisfies the pumping lemma. If the language does not satisfy the pumping lemma, show how to construct a string that breaks the pumping lemma. Show it for at least two values of candidates for the pumping length.
- whether it is regular (note that some languages that satisfy the pumping lemma may still be non-regular). Justify your answer, either by explaining why the language is regular, or by giving your intuition for why it is not regular. You don't need to do a proof.

The languages to try:

- The 6th example (the language a^n b^j a^k, where n > 5, j > 3, and k ≤ j). Choose the "computer goes first" option so that you are trying to prove that the language is non-regular.
- The 8th example (the language a^n b^k, n is odd or k is even). Choose the "you go first" option so that you are trying to prove that the language satisfies the pumping lemma.

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